igGameCenter API Developer Guide >> List of available games and their IDs
IDGameInternal Name 
1Chess chess
2Checkers (International) checkers_ing
3Checkers (English) checkers_eng
4Checkers (Russian) checkers_rus
5Halma halma
6Reversi reversi more details
7Renju renju more details
8Battleship battleship
9Kalah kalah more details
10Backgammon bckgmn
11Crosslet crosslet
12Hex hex